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E-book
Large Deviations for Gaussian Queues: Modelling Communication NetworksISBN: 978-0-470-51508-2
E-book
336 pages
April 2007
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1 Introduction.
Part A: Gaussian traffic and large deviations.
2 The Gaussian source model.
2.1 Modeling network traffic.
2.2 Notation and preliminaries on Gaussian random variables.
2.3 Gaussian sources.
2.4 Generic examples-long-range dependence and smoothness.
2.5 Other useful Gaussian source models.
2.6 Applicability of Gaussian source models for network traffic.
3 Gaussian sources: validation, justification.
3.1 Validation.
3.2 Convergence of on-off traffic to a Gaussian process.
4 Large deviations for Gaussian processes.
4.1 Cram´er's theorem.
4.2 Schilder's theorem.
Part B: Large deviations of Gaussian queues.
5 Gaussian queues: an introduction.
5.1 Lindley's recursion, the steady-state buffer content.
5.2 Gaussian queues.
5.3 Special cases: Brownian motion and Brownian bridge.
5.4 A powerful approximation.
5.5 Asymptotics.
5.6 Large-buffer asymptotics.
6 Logarithmic many-sources asymptotics.
6.1 Many-sources asymptotics: the loss curve.
6.2 Duality between loss curve and variance function.
6.3 The buffer-bandwidth curve is convex.
7 Exact many-sources asymptotics.
7.1 Slotted time: results.
7.2 Slotted time: proofs.
7.3 Continuous time: results.
7.4 Continuous time: proofs.
8 Simulation.
8.1 Determining the simulation horizon.
8.2 Importance sampling algorithms.
8.3 Asymptotic efficiency.
8.4 Efficient estimation of the overflow probability.
9 Tandem and priority queues.
9.1 Tandem: model and preliminaries.
9.2 Tandem: lower bound on the decay rate.
9.3 Tandem: tightness of the decay rate.
9.4 Tandem: properties of the input rate path.
9.5 Tandem: examples.
9.6 Priority queues.
10 Generalized processor sharing.
10.1 Preliminaries on GPS.
10.2 Generic upper and lower bound on the overflow probability.
10.3 Lower bound on the decay rate: class 2 in underload.
10.4 Upper bound on the decay rate: class 2 in underload.
10.5 Analysis of the decay rate: class 2 in overload.
10.6 Discussion of the results.
10.7 Delay asymptotics.
11 Explicit results for short-range dependent inputs.
11.1 Asymptotically linear variance; some preliminaries.
11.2 Tandem queue with srd input.
11.3 Priority queue with srd input.
11.4 GPS queue with srd input.
11.5 Concluding remarks.
12 Brownian queues.
12.1 Single queue: detailed results.
12.2 Tandem: distribution of the downstream queue.
12.3 Tandem: joint distribution.
Part C: Applications.
13 Weight setting in GPS.
13.1 An optimal partitioning approach to weight setting.
13.2 Approximation of the overflow probabilities.
13.3 Fixed weights.
13.4 Realizable region.
14 A link dimensioning formula and empirical support.
14.1 Objectives, modeling, and analysis.
14.2 Numerical study.
14.3 Empirical study.
14.4 Implementation aspects.
15 Link dimensioning: indirect variance estimation.
15.1 Theoretical foundations.
15.2 Implementation issues.
15.3 Error analysis of the inversion procedure.
15.4 Validation.
16 A framework for bandwidth trading.
16.1 Bandwidth trading.
16.2 Model and preliminaries.
16.3 Single-link network.
16.4 Gaussian traffic; utility as a function of loss.
16.5 Sanov's theorem and its inverse.
16.6 Estimation of loss probabilities.
16.7 Numerical example.
Bibliography.
Index.
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